A point on the periphery of rotating disc has its acceleration vector making on angle 30° with velocity vector then the ratio of magnitude of centripetal acceleration to tangential acceleration is :
A stone is moved round a horizontal circle with a 20 cm long string tied to If centripetal acceleration is 9.8 m/s2, then its angular velocity will be :
Centripetal Acceleration is given by a= ω²R
⇒ 9.8 = ω²× 1/5
⇒ ω² =49
⇒ ω = 7 rad/sec
A block on a stationary horizontal table with increasing speed in a circle is seen from an inertial frame of reference. The angle between net force on the block and velocity vector is :
When net acceleration makes acute angle with velocity, speed of the particle will increase. As tangential accleration is positive, speed will increase.
A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first 2 sec, it rotates through an angle θ1; in the next 4 sec, it rotates through an additional angle θ2. The ratio of θ2/θ1 is :
For Circular motion angle traversed is θ = ω t + ½ α t²
so, θ1 =½α(2)² = 2α
and θ1 + θ2 = ½α(6)² = 18 α ⇒ θ2= 16 α
so θ2 /θ1= 8
A wheel having diameter of 3 m starts from rest and accelerates uniformly to an angular velocity of 210 rpm in 5 seconds. Angular acceleration of the wheel is :
The angular velocity of earth about its axis of rotation is :
Angular speed ω = 2π / T = 2π / (60×60×24) rad /sec
Two bodies of masses 10 kg and 5 kg moving on concentric orbits of radii R and r such that their period of revolution are same. The ratio of their centripetal acceleration is :
As time period of revolution is same for both the particles angular speed will be equal for both.
Centripetal Acceleration is given by ω²r.
so a 1 / a 2 = R/r
A stone of mass m is tied to a string of length l and rotated in a circle with a constant speed v. If the string is released, the stone flies :
In Circular motion velocity of the particle is always directed along tangent. So when string is released object moves tangentially.
A car has to move on a level turn of radius (R = 50m). If the coefficient of static friction between tyre and road is µ = 0.2. Find the maximum speed the car can take without skidding is given by :
For safe turning on a horizontal road.
μ = v²/ rg ⇒ v= (μ rg ) 1/2
v = (0.2 × 50 × 10 ) 1/2 = 10 m/s
A coin placed on a rotating turntable just slips if it is placed at a distance of 4 cm from the If the angular velocity of the turntable is doubled, it will just slip at a distance of :
F= mω²r
As the distance will increase centrifugal force acting on the object will also increase. As slipping starts at 4 cm object will not slip at radius smaller than 4cm.
